A particular city is serviced by two airlines for its passen

A particular city is serviced by two airlines for its passenger trac. Airline A carries 70% of the passengers and Airline B carries the remaining 30%. The probabilities that a passenger reaches his/her destination on time ying Airlines A is 0.8 and fying Airline B is 0.4

(a) What is the probability that a passenger will reach his/her destination late?

(b) If a passenger was late in reaching her destination, what is the probability that she flew Airline B?

Solution

a. Arriving late can be due to either of the airlines.

Due to A, 0.7*0.2. Due to B, 0.3*0.6

P(x) = 0.32

b. Arriving late due to B, X = event

P(Bx) = 0.18

P(BuX) = .18 + .14 = 0.32

P( B|X) = 0.18/0.32 = 0.5625